MANBIJ, Syria -- Two senior American generals came to the front line outside the Syrian city of Manbij on Wednesday flying outsized American flags on their vehicles, in case pro-Turkish forces just the other side of the no man's land, 20 yards away, did not realize who they were.

"We're very proud of our positions here, and we want to make sure everybody knows it," said Maj. Gen. Jamie Jarrard, the Special Operations commander for the American-led coalition in Iraq and Syria.

If the message to Turkey was not clear already, the overall coalition commander accompanying General Jarrard, Lt. Gen. Paul Funk, elaborated. "You hit us, we will respond aggressively. We will defend ourselves."

The trip was the first by such senior United States military officers to the front in northern Syria since Turkey's president threatened to attack the city of Manbij, calling it a bastion of terrorists and demanding that American forces leave.

But the Americans have refused, creating the potential for an unprecedented armed conflict between two NATO allies, the United States and Turkey -- the latest twist on the seven-year-old war in Syria.

This part of Syria's north was once overrun by Islamic State militants. The United States and its allies, Syrian Kurdish fighters, collaborated more than a year ago to evict them.

But in the effort, the United States angered Turkey, which has long regarded the Kurds as enemies. Now the Turks are turning their guns on the Kurds, setting up a possible fight with the Americans.

General Funk had an automatic pistol slung across his vest. His three uniform stars would have been easily visible with binoculars to the Syrian militias aligned with Turkey on the other side of the front line, as he stood on a sandbagged roof. He was surrounded by Special Forces soldiers, and Arab and Kurdish fighters from the Manbij Military Council, the government authority in the region.

The two generals arrived at the border post in unarmored cars, in an entourage that included several mine-resistant armored personnel carriers, as well as Land Cruisers for Special Forces soldiers, with antennas, spare tires and jerrycans on their roofs.

Manbij is the farthest west that the Americans, aligned with the Syrian Democratic Forces insurgent group in the fight against the Islamic State, are stationed.

Showing off the Stars and Stripes in this city is not at all extraordinary. American military vehicles usually fly flags on what they call de-escalation patrols through the city and province of Manbij. The patrols are so frequent that children have learned to flash the thumb-and-little finger wiggle gesture popularized by American soldiers.

Women in full chadors smile and wave at their convoys, and American soldiers even visit the crowded bazaar in unarmored cars, disembarking on foot with only sidearms, according to locals -- unusual for any place at risk of an Islamic State attack. "I would feel very comfortable anywhere in northeastern Syria," General Jarrard said.

Similarly the relationship between the Americans and the Manbij Military Council is comfortable and cordial, and the Americans have praised its efforts to restore a stable government. Standing on the front-line rooftop, General Funk addressed the military council's commander, Muhammed Abu Adel: "The lasting defeat of ISIS is the most important mission for this group," he told Commander Adel, a Kurd, although the majority of his fighters are local Arabs. "It's in your hands now and you're doing a good job. One team, one fight."

Commander Adel thanked him, and said he hoped American air power would continue to assist his forces. The general did not respond directly.

The American support for Manbij has particularly alarmed Turkey. It is waging a military campaign to take the Kurdish-held city of Afrin, 80 miles west, while pursuing an unusually outspoken public relations campaign to threaten Manbij and make the Americans depart, so that Syrian militias aligned with Turkish forces can take it from America's Kurdish-led allies.

On Tuesday, once again, President Recep Tayyip Erdogan of Turkey criticized the American support of Manbij. "They tell us, 'Don't come to Manbij.' We will come to Manbij to hand over these territories to their rightful owners," Mr. Erdogan said in a speech to his party. The Turkish deputy prime minister went so far as to suggest American troops in Manbij are wearing uniforms of the Kurdish People's Protection Forces, or Y.P.G., and said they could become targets.

The Y.P.G. dominates Kurdish areas of northern Syria and is the main component of the Syrian Democratic Forces, the American allies in the fight against the Islamic State, also known as ISIS and Daesh.

But in Manbij, both the Americans and the Kurds insist, the defending force is the Manbij Military Council, an ally of the Syrian Democratic Forces, but independent and composed mostly of Arab fighters.

The Turks depict the Y.P.G. as a version of the outlawed Kurdistan Workers' Party or P.K.K., a separatist group regarded as a terrorist organization by the United States and Europe.

"If we are terrorist," said Commander Adel, during the generals' visit Wednesday, "O.K., then all of the countries in the coalition and these American soldiers here are terrorist too?" The American-led anti-ISIS coalition has more than 70 member countries.

The Turks say the Manbij Military Council is just the Y.P.G. in disguise. The Americans and Kurds say the council is allied with the Kurdish-dominated Syrian Democratic Forces, but most of its fighters are local Arabs.

The American military has sought to persuade Turkey that the Manbij forces are reliable allies, and important in the fight against ISIS elsewhere. Previously, the Americans hosted meetings between Turkish military officers and Manbij officers to try to convince them, but those meetings ceased this year. General Funk said the Turks had declined an invitation to Manbij this year.

Last month President Erdogan was infuriated when the Americans announced they were forming a 30,000-strong permanent border protection force in Kurd-held areas as a long-term way to fight ISIS, using the Syrian Democratic Forces. On Jan. 20, the Turks responded with an offensive against Afrin, threatening to continue on straight across northern Syria. "The U.S. says that they have cleared Daesh from Syria," Mr. Erdogan said Tuesday. "Why are you still here?"

The Americans say the fight against ISIS is far from over in Syria, even though the group has been expelled from all urban areas, like Manbij, which the Americans and their Syrian allies cleared in the summer of 2016.

The Americans have vowed to stay in Manbij and support their allies. But the American forces in Manbij number only a few hundred out of a total of 2,000 in all of northern Syria, mostly Special Operations troops. The Turks and their allied militias, the Free Syrian Army fighting around Afrin, are estimated at 20,000 in all. Both Turks and Americans have substantial air forces in the area.

Even if the Turks do not carry out their threats, the fight in Afrin has indirectly hurt the American-led fight against ISIS. As the Syrian Democratic Forces shift fighters to the battle in Afrin, they have weakened the ISIS campaign far to the east.

"It's illogical that while we are fighting ISIS, the enemy of the world, over there, the Turks attack us in Afrin," said Shervan Derwish, the spokesman for the Manbij Military Council. "Our fight against ISIS has had to be minimized as we reduce our power there to defend Afrin."

The military council, supported by American Special Operations troops and air power, defeated ISIS in Manbij in August 2016, and then established a local government administration that has controlled the area since. "Before they got here, this was a highway for Islamist terrorist fighters into the physical caliphate from all over the world," General Jarrard said.

The council remains an important part of the effort to fight ISIS, with many of its fighters alongside American forces in the eastern part of the country, where the last pockets of ISIS control remain.

American policymakers worry that the Afrin conflict, and the threat against Manbij, will degrade their Kurdish and Arab allies.

"I think our main concern is that anything that disrupts everybody's focus on ISIS and eliminating the complete physical caliphate -- and we're close, we're very close -- something people couldn't have imagined a year ago -- anything that disrupts us or takes our eye off that prize, is not good," General Jarrard said.

General Funk said the Americans prefer to "maintain focus on the enemy in front of you and mow him down -- that's much easier than having to look in multiple directions."

In Manbij, initial alarm at the Turkish threats has dissipated as the Turkish campaign against Afrin, which the Turks had vowed to overrun in a few days, has dragged into a third week.

The local civil government is modeled on principles of the Kurdish separatist leader, Abdullah Ocalan, who is imprisoned in Turkey: enforced equality for women in civil and military life, moderate socialism, and radical environmentalism.

The Turks' view is that the Kurds have imposed a system of governance in Manbij at odds with the area's conservative, traditional society. The American military, however, says that the Kurds and their allies have managed to bring stability. "There are a lot of people that do equate them with the P.K.K., but I have not seen any indication of that in my dealings with them throughout our relationship," General Jarrard said.

There is little doubt that the bulk of Manbij soldiers are Arabs, but their key leaders are Kurdish, with backgrounds in the Y.P.G. The Manbij Military Council leader, Muhammed Abu Adel, is Kurdish, as is Mr. Derwish, the council's influential spokesman, who has a prominent photograph of Abdullah Ocalan on the wall of his office.

"What's strange to me is that Turkey, as a member of NATO, is making this war against us under the name of jihad, but we are only democrats," Mr. Derwish said. "In our society, women are free, we have equality and democracy. And they want to destroy us."

General Funk, a veteran of Iraq and other deployments, said Syria had been "delightful" by comparison. "People are trying to get back to their normal way of living," he said. "As long as people keep working together on that local governance and local control, I see hope."